If chondrules were exposed to cosmic rays prior to meteorite compaction, they should retain an excess of cosmogenic noble gases. Beyersdorf-Kuis et al. (2015) showed that such excesses can be detected provided that the chemical composition of each individual chondrule is precisely known. However, their study was limited to a few samples as they had to be irradiated in a nuclear reactor for instrumental neutron activation analysis. We developed a novel analytical protocol that combines the measurements of He and Ne isotopic concentrations with a fast method to correct for differences in chemical composition using micro X-ray computed tomography. Our main idea is to combine noble gas, nuclear track, and petrography data for numerous chondrules to understand the precompaction exposure history of the chondrite parent bodies. Here, we report our results for a total of 77 chondrules and four matrix samples from NWA 8276 (L3.00), NWA 8007 (L3.2), and Bjurböle (L/LL4). All chondrules from the same meteorite have within uncertainty identical 21Ne exposure ages, and all chondrules from Bjurböle have within uncertainty identical 3He exposure ages. However, most chondrules from NWA 8276 and a few from NWA 8007 show small but resolvable differences in 3He exposure age that we attribute to matrix contamination and/or gas loss. The finding that none of the chondrules has noble gas excesses is consistent with the uniform track density found for each meteorite. We conclude that the studied chondrules did not experience a precompaction exposure longer than a few Ma assuming present-day flux of galactic cosmic rays. A majority of chondrules from L and LL chondrites thus rapidly accreted and/or was efficiently shielded from cosmic rays in the solar nebula.